\(C=1+3+3^2+3^3+...+3^{19}+3^{20}\)
\(3.C=3+3^2+3^3+3^4+...+3^{20}+3^{21}\)
\(3.C-C=3^{21}-1\)
\(\Rightarrow C=\frac{3^{21}-1}{2}\)
\(D=\)\(5+5^2+5^3+...+5^{99}+5^{100}\)
\(5.D=5^2+5^3+5^4+...+5^{100}+5^{101}\)
\(5.D-D=5^{101}-5\)
\(\Rightarrow D=\frac{5^{101}-5}{4}\)
\(C=1+3+3^2+...+3^{20}\)
\(3C=3+3^2+3^3+...+3^{21}\)
\(3C-C=\left(3+3^2+3^3+...+3^{21}\right)-\left(1+3+3^2+...+3^{20}\right)\)
\(2C=\left(3-3\right)+\left(3^2-3^2\right)+\left(3^3-3^3\right)+...+\left(3^{20}-3^{20}\right)+3^{21}-1\)
\(2C=3^{21}-1\)
\(C=\frac{3^{21}-1}{2}\)
\(D=5+5^2+5^3+...+5^{100}\)
\(5D=5^2+5^3+5^4+...+5^{101}\)
\(5D-D=\left(5^2+5^3+5^4+...+5^{101}\right)-\left(5+5^2+5^3+...+5^{100}\right)\)
\(4D=\left(5^2-5^2\right)+\left(5^3-5^3\right)+\left(5^4-5^4\right)+...+\left(5^{100}-5^{100}\right)+5^{101}-5\)
\(4D=5^{101}-5\)
\(D=\frac{5\left(5^{100}-1\right)}{4}=\frac{5}{4}\left(5^{100}-1\right)\)
